A tour group split into two groups when waiting in line for food at a fast food counter.

Question

A tour group split into two groups when waiting in line for food at a fast food counter. the first group bought 8 slices of pizza and 5 soft drinks for $27.71. The second group bought 4 slices of pizza and 3 soft drinks for $14.57. How much does a slice of pizza cost? How much does a soft drink cost?

Answer 1

There are two variables here - p the number of slices of pizza, and s the number of soft drinks.

From the given information you can set up the following two equations:

8p + 5s = 27.71

4p + 3s = 14.57

Now you want to solve for one of the variables by eliminating a variable. Notice that if you multiply the second equation by 2, the system becomes

8p + 5s = 27.71

8p + 6s = 29.14

Then, you can subtract the first equation from the second obtaining s = 1.43.

Now you can plug s = 1.43 into either of the equations to obtain p.

If you plug it into the first equation you have 8p + 5(1.43) = 27.71

8p + 7.15 = 27.71

8p = 20.56

p = 2.57

Thus, a slice of pizza costs $2.57 and a soft drink costs $1.43.